denis_kos

Very strange behavior. So you are connecting the TT Sync controller to the Phantek case's RGB header of some sort, not the motherboard?

Are you trying to control the fans with the remote or through motherboard software? It says that the built in controller is compatible with MSI and Asus RGB software. So in theory I would think it should be fine if you're motherboard is interfacing with that controller. If Phantek's built in settings are in control, then that is probably your issue.
An easy way to check that you didn't receive any bad equipment is to connect it directly to a 5V RGB header on your motherboard and see it functions correctly that way.

That's unfortunate that you don't have an RGB header. It makes things more difficult to troubleshoot.
It may be the case that Phantek's controller interprets the ASUS and MSI software signals to protocols that their RGB products will understand. In which case, if that controller is not outputting ASUS or MSI RGB protocols, that could explain the abnormal behavior as the TT Sync controller would not be designed to handle Phantek's protocols. 
You have PWM cables running between the TT Sync controller and the motherboard, correct? Those are what actually drive the fans and pump. Connecting to the TT Sync controller to an RGB header (or in your case the built in Phantek controller) is just for the lights.
You would have to ask Phantek about about this more in depth.

How do you have the devices plugged into the TT Sync controller? Per this user's thread, they had issues until they put the pump on its owner side of the controller:
 
If this still doesn't solve your issue you could try an RMA, but Thermaltake may just blow it off as incompatible products.